SOLUTION
Write out the function given
[tex]\begin{gathered} f(x)=3x+4 \\ \text{and } \\ g(x)=x^2-6x+5 \end{gathered}[/tex]The operation is multiplication
Hence we multiply the two functions
[tex]\begin{gathered} f(x)\text{.g(x)} \\ (3x+4)(x^2-6x+5) \\ \text{Expand the paranthesis} \\ 3x(x^2-6x+5)+4(x^2-6x+5) \end{gathered}[/tex]Then multiply each of the terms
[tex]\begin{gathered} 3x(x^2-6x+5)+4(x^2-6x+5) \\ 3x^3-18x^2+15x+4x^2-24x+20 \\ \text{collect like terms and simplify } \\ 3x^3-18x^2+4x^2+15x^{}-24x+20 \\ 3x^3-14x^2-9x+20 \end{gathered}[/tex]Hence
[tex]f(x)\text{.g(x)}=3x^3-14x^2-9x+20[/tex]The domain of a function are the set of values of x for which the function is define or real
For the function f(x).g(x), there is no undefine point or domain constraint fpor the function,
hence
[tex]\begin{gathered} \text{The domain is } \\ (-\infty,\infty) \end{gathered}[/tex]Therefore
f(x).g(x)= 3x³-24x²-9x+20
The domain is (-∞,∞)
